Decision concordance with incomplete expert rankings in manufacturing applications
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ORIGINAL PAPER
Decision concordance with incomplete expert rankings in manufacturing applications Fiorenzo Franceschini1 · Domenico Maisano1 Received: 23 July 2019 / Revised: 9 April 2020 / Accepted: 13 April 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The manufacturing field encompasses a number of problems in which some experts formulate their rankings of a set of objects, which should be aggregated into a collective judgment. For example, consider the aggregation of (1) the opinions of designers on alternative design concepts, (2) the opinions of reliability/safety engineers on the criticality of a set of failures, (3) the perceptions of a panel of customers on alternative aesthetic features of a product, etc. For these problems, Kendall’s concordance coefficient (W) can be used to express the degree of agreement between experts in a simple and practical way. Unfortunately, this indicator is applicable to complete rankings only, while experts often find it more practical to formulate incomplete rankings, e.g., identifying only the most/less relevant objects and/or deliberately excluding some of them, if they are not sufficiently relevant or well known. This research aims at extending the use of the traditional W to incomplete rankings, preserving its practical meaning and simplicity. In a nutshell, the proposed methodological approach associates a so-called “midrank” to all objects, even the ones that are not easily comparable with the other ones; subsequently, W can be applied to these midranks. The description is supported by several pedagogical examples. Keywords Incomplete ranking · Incomparability · Coefficient of concordance · Midrank · Degree of completeness
1 Introduction A widely debated problem in the scientific literature is that of “m-rankings”, in which each of m experts formulates his/her own (subjective) ranking of n objects, based on the degree of an attribute of these objects; then, rankings have to be aggregated into a collective judgment (Kendall and Smith 1939; Kendall 1963; Keeney and Raiffa 1993; Agresti 2010). This problem of wide cross-cutting nature is debated in various scientific fields, ranging from decision science to social choice theory, psychometrics, voting theory, multicriteria decision making, etc. (Kelly 1991; Tideman and Plassmann 2012; Coaley 2014). This problem is also debated in the manufacturing field: let us consider, for example, the aggregation of (1) the opinions of different designers on * Fiorenzo Franceschini [email protected] Domenico Maisano [email protected] 1
DIGEP (Department of Management and Production Engineering), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
some alternative design concepts, or (2) the opinions of maintenance/reliability experts on the more critical failures of a production process, or (3) the opinions of a panel of service/product customers on the degree of importance of some customer needs (Nahm et al. 2013; Franceschini et al. 2015; Franceschini et a
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